Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 4 (2016), 2325-2363.
Hopf algebras and invariants of the Johnson cokernel
We show that if is a cocommutative Hopf algebra, then there is a natural action of on which induces an action on a quotient . In the case when is the tensor algebra, we show that the invariant of the cokernel of the Johnson homomorphism studied in Algebr. Geom. Topol. 15 (2015) 801–821 projects to take values in . We analyze the case, getting large families of obstructions generalizing the abelianization obstructions of Geom. Dedicata 176 (2015) 345–374.
Algebr. Geom. Topol., Volume 16, Number 4 (2016), 2325-2363.
Received: 17 September 2015
Revised: 20 January 2016
Accepted: 24 January 2016
First available in Project Euclid: 28 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20J06: Cohomology of groups 16T05: Hopf algebras and their applications [See also 16S40, 57T05] 17B40: Automorphisms, derivations, other operators
Secondary: 20C15: Ordinary representations and characters 20F28: Automorphism groups of groups [See also 20E36]
Conant, Jim; Kassabov, Martin. Hopf algebras and invariants of the Johnson cokernel. Algebr. Geom. Topol. 16 (2016), no. 4, 2325--2363. doi:10.2140/agt.2016.16.2325. https://projecteuclid.org/euclid.agt/1511895916